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# Advanced Math/Finding total water volume in a cylinder based on exit flow rate.

Question
QUESTION: Is it possible to calculate the amount of water in a cylinder based off of the information that I have.
I have the exit pipe diameter
I have the rate of flow coming out of said pipe
I have the circumference and can get the height of said cylinder
I was able to calculate velocity based on pipe diameter and flow rate.

I need to be able to calculate the total amount of water "or rough percentage" based on what i have, or other information i may be able to gather. Is this possible?

the equation for the pressure of water flow is
P = pgh {where the p is really a greek rho}.

Now p is the pressure of the water at that point,
g is the gravitational constant, and
h is the height of the water.

You can calculate the liters exiting per minute based on finding the area of the circle (calculated from the raidus r as πr²) and how fast the water is coming out.

Since you have said the P and p are known, and g is known as well, this means that h can be calculated.  The equation of this is h = P/(pg).

---------- FOLLOW-UP ----------

QUESTION: I'm not sure I understand how to calculate P.

p and g i understand "i believe" 9.81 and 1,000.

But I don't understand what P represents and how to get it.

We have P = pgh { where is p is used for rho }.  In this equation, P is pressure in Pa,
p is the density in kg/m^3, g is gravity (9.81m/s²), and h is the depth of the liquid.

Now Pa in this equation is the pressure in terms of N/m² where N is Newtons and m is for meters.
A Newton in this equation is in the form of kg/s².

I believe p and g are given in reverse, for I know gravity is 9.81m/s².
Form this, it looks like p is 1,000kg/m³.

To get P, it looks like we need to integrate pgh for p = 0 (at the surface) to p = B
(B is the distance in meters to the bottom of the tank in terms of h.
That means there is a dh at the end of the integral.

When this is integrated, the answer is pgB²/2.

Volunteer

#### Scott A Wilson

##### Expertise

I can answer any question in general math, arithetic, discret math, algebra, box problems, geometry, filling a tank with water, trigonometry, pre-calculus, linear algebra, complex mathematics, probability, statistics, and most of anything else that relates to math. I can also say that I broke 5 minutes for a mile, which is over 12 mph, but is that relevant?

##### Experience

Experience in the area; I have tutored people in the above areas of mathematics for over two years in AllExperts.com. I have tutored people here and there in mathematics since before I received a BS degree back in 1984. In just two more years, I received an MS degree as well, but more on that later. I tutored at OSU in the math center for all six years I was there. Most students offering assistance were juniors, seniors, or graduate students. I was allowed to tutor as a freshman. I tutored at Mathnasium for well over a year. I worked at The Boeing Company for over 5 years. I received an MS degreee in Mathematics from Oregon State Univeristy. The classes I took were over 100 hours of upper division credits in mathematical courses such as calculus, statistics, probabilty, linear algrebra, powers, linear regression, matrices, and more. I graduated with honors in both my BS and MS degrees. Past/Present Clients: College Students at Oregon State University, various math people since college, over 7,500 people on the PC from the US and rest the world.

Publications
My master's paper was published in the OSU journal. The subject of it was Numerical Analysis used in shock waves and rarefaction fans. It dealt with discontinuities that arose over time. They were solved using the Leap Frog method. That method was used and improvements of it were shown. The improvements were by Enquist-Osher, Godunov, and Lax-Wendroff.

Education/Credentials
Master of Science at OSU with high honors in mathematics. Bachelor of Science at OSU with high honors in mathematical sciences. This degree involved mathematics, statistics, and computer science. I also took sophmore level physics and chemistry while I was attending college. On the side I took raquetball, but that's still not relevant.

Awards and Honors
I earned high honors in both my BS degree and MS degree from Oregon State. I was in near the top in most of my classes. In several classes in mathematics, I was first. In a class of over 100 students, I was always one of the first ones to complete the test. I graduated with well over 50 credits in upper division mathematics.

Past/Present Clients
My clients have been students at OSU, people who live nearby, friends with math questions, and several people every day on the PC. I would guess that you are probably going to be one more.